**Question:**

The value of *p* for which the polynomial x3 + 4x2 − px + 8 is exactly divisible by (x−2) is

(a) 0

(b) 3

(c) 5

(d) 16

**Solution:**

Here the given polynomial is $x^{3}+4 x^{2}-p x+8$

We have to find the value of *p* such that the polynomial is exactly divisible by

First we have to write equation in basic format of divisibility like this

$x^{3}-2 x^{2}$

$6 x^{2}-p x+8$

$6 x^{2}-12 x$

$12 x-p x+8$

$\frac{4 x+8}{16 x-p x}$

After solving, we have seeing here the reminder is = 16*x* − *px*

So, to find the value of *p*** **we put the reminder is equal to zero.

Therefore

$16 x-p x=0$

$\Rightarrow \quad 16 x=p x$

$\Rightarrow \quad p=16$

Hence option (*d*) is correct.